the best periods of Greek music these refinements of melody, which modern musicians find scarcely conceivable, were far from being accidental or subordinate features. Rather, they were as much bound up with the fundamental nature of that music as complex harmony is with the music of modern Europe. [Footnote 1: Aristox. _Harm._ p. 23 Meib. [Greek: hoi men gar tê nun katechousê melopoiia ounêtheis monon ontes eiktôs tên ditonon lichanon] (_f_ in the scale _e-a_) [Greek: exorizousi; suntonôterais gar chrôntai schedon hoi pleistoi tôn nun. toutou d' aition to boulesthai glukainein aei. sêmeion de hoti toutou stochazontai, malista men gar kai pleiston chronon en tô chrômati diatribousin. hotan d' aphikôntai pote eis tên harmonian engus tou chromatos prosagousi, sunepismômenou tou êthous.]] [Footnote 2: Ibid. p. 26 [Greek: noêteon gar apeirous ton arithmon tas lichanous. hou gar an stêsês tên phônên apodedeigmenon lichanô topou lichanos estai; diakenon de ouden esti tou lichanoeidous topou, oude toiouton hôste mê dechisthai lichanon]. And p. 48 [Greek: epeidê per ho tês lichanou topos eis apeirous temnetai tomas].] [Footnote 3: Aristox. _Harm._ p. 69 Meib. [Greek: kata men oun ta megethê tôn diastêmatôn kai tas tôn phthongôn taseis apeira pôs phainetai einai ta peri to melos, kata de tas dynameis kai kata ta eidê kai kata tas theseis peperasmena te kai tetagmena.]] The mediaeval modes or Tones, on the other hand, are essentially based on the diatonic scale,--the scale that knows only of tones and semitones. To suppose that they held in the earliest Greek music the prominent place which we find assigned to the ancient Modes or [Greek: harmoniai] is to suppose that the art of music was developed in Greece in two different directions, under the influence of different and almost opposite ideas. Yet nothing is more remarkable in all departments of Greek art than the strictness with which it confines itself within the limits given once for all in the leading types, and the consequent harmony and consistency of all the forms which it takes in the course of its growth. The dependence of artistic forms in their manifold developments upon a central governing idea or principle has never been more luminously stated than by the illustrious physicist Helmholtz, in the thirteenth chapter of his _Tonempfindungen_. I venture to think that in applying that truth to the facts of Greek music he was materially hindered by the accepted theory of the Greek modes. The scales which he analyses under that name were certainly the basis of all music in the Middle Ages, and are much more intelligible as such than in relation to the primitive Greek forms of the art[1].